A dispersionless algorithm for calculating wake potentials in 3D

Abstract

Accurate computations of wake potentials are an important task in modern accelerator design. Short bunches used in high energy particle accelerators excite very highfrequency fields. The geometrical size of accelerating structures exceeds the wavelength of the excited fields by many orders of magnitude. The application of codes such as TBCI, MAFIA[1] or tamBCI are limited due to numerical dispersion effects and memory needs. Recently new codes like PBCI have been developed to overcome these problems. In this work the utilization of dispersionless directions in the leapfrog update scheme on a Cartesian grid are proposed for accurate simulations. In conjunction with a conformal modeling technique which allows for the full Courant time step a moving window technique can be applied. This was previously implemented in a 2D code [2]. In this publication an extension to arbitrary three dimensional problems is presented.

Three-Dimensional Wake Field Computations Based on Scattered-Field Time Domain Boundary Element Method

“…The two tangential components and the normal component of the magnetic field are appeared in the MFIE (7). Unlike the axisymmetric 2-D S-TDBEM scheme [12], the normal component of the magnetic fields does not vanish in full 3-D schemes, but it is not unknown boundary value because of the boundary conditions (8).…”

“…However, in recent accelerator applications the following problems are recognized to be difficult even with such FIT-based approaches: short-range wake field simulations of a short bunch in long accelerator structures and transient analysis of wake fields excited by a bunch moving with curved trajectories in arbitrarily shaped 3-D vacuum chambers. For the former, several dispersionless algorithms have been proposed in the context of FIT [4]- [7]. In the latter, however, the applicability of the existing FIT/FEM codes may be still severely limited by the numerical dispersion errors of finite difference scheme used in their codes.…”

Time Domain Boundary Element Analysis of Wake Fields in Long Accelerator Structures

“…BOUNDARY ELEMENT METHOD In order to compute the short-range wake fields of a short bunch traversing long accelerator structures at low calculation costs, a moving window technique [12] has been used in Finite Integration Technique (FIT) codes such as TBCI [20], ECHO [21], PBCI [22], and ROCOCO [23]. For the same purpose, we incorporate the concept of this technique into the TDBEM scheme.…”

“…Fig. 7 shows the comparison of wake potentials computed by the proposed scheme and the code ROCOCO [23] for ultra short bunch with . The ROCOCO result for is regarded as the reference solution.…”